Using Kummer theory for a finite extension K of \Qp(\zeta)(where p is a prime
number and \zeta a primitive p-th root of~1), we compute the ramification
filtration and the discriminant of an arbitrary elementary abelian p-extension
of K. We also develop the analogous Artin-Schreier theory for finite extensions
of \Fp((\pi)) and derive similar results for their elementary abelian
p-extensions.